Rounded caps on a Bezier Curve pipe
Increase curve resolution

As stated in the Blender Artist thread you linked, you'll need to guarantee enough resolution to your curve in order to see the effect of the taper object in the starting and ending tip. In your image you are using something like 12, while the following image has a value of 512.



If you need to keep the polycount low, you could also vary the resolution of the curve only locally. A possible workaround could be yo interpose a "strategic" handle very near the tip without altering the overall curve aspect. See the difference between the had and the tail in the image below despite the curve object resolution is left untouched. The following curve has 3, not two handlers: